To add the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{8}{9}\)[/tex], we need to follow a step-by-step approach:
1. Find the Least Common Denominator (LCD):
The denominators of the fractions are 6 and 9. The least common multiple (LCM) of 6 and 9 is 18, which will be our LCD.
2. Convert each fraction to have the same denominator:
- For [tex]\(\frac{5}{6}\)[/tex]: Multiply both the numerator and the denominator by [tex]\(3\)[/tex] to get [tex]\(\frac{5 \times 3}{6 \times 3} = \frac{15}{18}\)[/tex].
- For [tex]\(\frac{8}{9}\)[/tex]: Multiply both the numerator and the denominator by [tex]\(2\)[/tex] to get [tex]\(\frac{8 \times 2}{9 \times 2} = \frac{16}{18}\)[/tex].
3. Add the numerators of the converted fractions:
Now that both fractions have the same denominator, simply add the numerators together:
[tex]\[
\frac{15}{18} + \frac{16}{18} = \frac{15 + 16}{18} = \frac{31}{18}
\][/tex]
4. Simplify the resulting fraction (if possible):
Check if the fraction [tex]\(\frac{31}{18}\)[/tex] can be simplified. The greatest common divisor (GCD) of 31 and 18 is 1, so the fraction [tex]\(\frac{31}{18}\)[/tex] is already in its simplest form.
So, the sum of the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{8}{9}\)[/tex] is:
[tex]\[
\frac{31}{18}
\][/tex]
